This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure & integration Presented in a definitive & self-contained manner it features a natural progression of concepts from simple to difficult Several innovative topics are featured including differentiation of measures elements of Functional Analysis the Riesz Representation Theorem Schwartz distributions the area formula Sobolev functions & applications to harmonic functions Together the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations This second edition of Modern Real Analysis contains many substantial improvements including the addition of problems for practicing techniques & an entirely new section devoted to the relationship between Lebesgue & improper integrals Aimed at graduate students with an understanding of advanced calculus the text will also appeal to more experienced mathematicians as a useful reference